In general, the game uses the plain english definition of Ability which means "The power or capability to do or act." So it's not really a game term, but the closest thing to a game definition that you will find can be found on page 11 of the English rules v3, where it talks about creatures having special abilities and these being "...described on their card or may appear as an 'ability bar' on there card." So, in general it is card text.
Now, the reason [mwcard=MWSTX1CKJ01]Enchanter's Wardstone[/mwcard] doesn't work against [mwcard=MWSTX2FFJ01]Harshforge Monolith[/mwcard] is because the Monolith's ability doesn't destroy the enchantment. It's ability simply adds a trait to the enchantment. It is then the Enchantment's own trait that is destroying it. Regardless of the fact that it was the Monolith that gave it the Upkeep +1 trait, it is the Enchantment that has the Upkeep +1 trait. So the enchantment is destroying itself with it's own trait.